Brinkman's law as $Γ$-limit of compressible low Mach Navier-Stokes equations and application to randomly perforated domains
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908367237152768 |
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| author | Bella, Peter Lemming, Friederike Marziani, Roberta Oschmann, Florian |
| author_facet | Bella, Peter Lemming, Friederike Marziani, Roberta Oschmann, Florian |
| contents | We consider the time-dependent compressible Navier-Stokes equations in the low Mach number regime inside a family of domains $(Ω_\varepsilon)_{\varepsilon > 0}$ in $\mathbb{R}^3$. Assuming that $\lim_{\varepsilon \to 0} Ω_\varepsilon = Ω\subset \mathbb{R}^3$ in a suitable sense, we show that in the limit the fluid flow inside $Ω$ is governed by the incompressible Navier-Stokes-Brinkman equations, provided the latter one admits a strong solution. The abstract convergence result is complemented with a stochastic homogenization result for randomly perforated domains in the critical regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brinkman's law as $Γ$-limit of compressible low Mach Navier-Stokes equations and application to randomly perforated domains Bella, Peter Lemming, Friederike Marziani, Roberta Oschmann, Florian Analysis of PDEs We consider the time-dependent compressible Navier-Stokes equations in the low Mach number regime inside a family of domains $(Ω_\varepsilon)_{\varepsilon > 0}$ in $\mathbb{R}^3$. Assuming that $\lim_{\varepsilon \to 0} Ω_\varepsilon = Ω\subset \mathbb{R}^3$ in a suitable sense, we show that in the limit the fluid flow inside $Ω$ is governed by the incompressible Navier-Stokes-Brinkman equations, provided the latter one admits a strong solution. The abstract convergence result is complemented with a stochastic homogenization result for randomly perforated domains in the critical regime. |
| title | Brinkman's law as $Γ$-limit of compressible low Mach Navier-Stokes equations and application to randomly perforated domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.11213 |